Question

given the information in the diagram, which theorem best justifies why lines e and f must be parallel?
○ alternate interior angles theorem
○ same side interior angles theorem
○ converse of the alternate interior angles theorem
○ converse of the same side interior angles theorem

Explanation:

First, identify the relationship between the given angles: $72^\circ + 108^\circ = 180^\circ$, so they are supplementary same-side interior angles. The original same-side interior angles theorem states that if two parallel lines are cut by a transversal, same-side interior angles are supplementary. We are using the reverse: knowing the same-side interior angles are supplementary to prove the lines are parallel, which is the converse of this theorem.

Answer:

converse of the same side interior angles theorem